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The Garden of Eden theorem for linear cellular automata

Published online by Cambridge University Press:  13 January 2006

TULLIO CECCHERINI-SILBERSTEIN  and
MICHEL COORNAERT
TULLIO CECCHERINI-SILBERSTEIN
Affiliation:
Dipartimento di Ingegneria, Università del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy (e-mail: tceccher@mat.uniroma1.it)
MICHEL COORNAERT
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France (e-mail: coornaert@math.u-strasbg.fr)
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Abstract

Let V be a finite-dimensional vector space over a field ${\mathbb{K}}$ and let G be a countable amenable group. Let $\tau \colon V^G \to V^G$ be a linear cellular automaton. We prove that $\tau$ is surjective if and only if it is pre-injective.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 1 , February 2006 , pp. 53 - 68
Copyright
2006 Cambridge University Press

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